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{{mainMain|mutation (genetic algorithm)}}

The [[genetic algorithm]] in [[economics]] is an [[algorithm]] used to [[Model (abstract)|model]] the [[learning behaviour]] of [[economic agents]]. The term "genetic algorithm" is often abbreviated as GA. The genetic algorithm is a particular class of [[evolutionary algorithm]] inspired by [[evolutionary biology]]. A genetic algorithm is defined as basic if it only contains a method for reproduction and experimentation. It is defined as augmented if it contains a selection operator as well.

The genetic'''[[Genetic algorithm]]s''' hashave increasingly been applied to economics oversince the lastpioneering twowork decadesby John H. Miller in 1986. It has been used to characterize a variety of models including the [[cobweb model]], the [[overlapping generations model]], [[game theory]], [[Genetic algorithm scheduling|schedule optimization]] and [[asset pricing]]. Specifically, it has been used as a model to represent learning, rather than as a means for fitting a model.

Genetic algorithms are useless.

== Genetic Algorithmalgorithm in the Cobwebcobweb Modelmodel ==

Genetic algorithms are [[Implementation|implement]]ed as a [[computer simulation]] in which a [[population]] of [[abstract]] representations (called [[chromosome (genetic algorithm)|chromosomes]] or strings) of [[candidate solutions]] (called individuals, or agents) to an optimization problem evolves toward better [[Solution (business)|solution]]s. Traditionally, solutions are represented in binary as strings of 0s and 1s, but other encodings are also possible. The evolution usually starts from a population of randomly generated individuals and happens in generations. In each generation, the fitness of every individual in the population is evaluated, multiple individuals are stochastically selected from the current population (based on their fitness), and modified (mutated or recombined) to form a new population. The new population is then used in the next iteration of the algorithm.

The [[cobweb model]] is a simple supply and demand model for a good over ''t'' periods. Firms (agents) make a production quantity decision in a given period, however their output is not produced until the following period. Thus, the firms are going to have to use some sort of method to forecast what the future price will be. The GA is used as a sort of learning behaviour for the firms. Initially their quantity production decisions are random, however each period they learn a little more. The result is the agents converge within the area of the [[rational expectations]] equilibrium (RATEX) equilibrium for the stable and unstable case. If the election operator is used, the GA converges exactly to the RATEX equilibrium.

The genetic algorithm has increasingly been applied to economics over the last two decades. It has been used to characterize a variety of models including the [[cobweb model]], the [[overlapping generations model]], [[game theory]] and [[asset pricing]]

There are two typetypes of learning methods these agents can be deployed with: social learning and individual learning. In social learning, each firm is endowed with a single string (which is used as its quantity production decision). It then compares this string against other firmfirms's strings. In the individual learning case, agents are endowed with a pool of strings. These strings are then compared against other strings within the agent's population pool. This can be thought of as mutual competing ideas within a firm whereas in the social case, it can be thought of as a firm's learning from more successful firms. Note that in the social case and in the individual learning case with identical cost functions, that this is a homogeneous solution, that is all agentagents's production decisions are identical. However, if the cost functions are not identical, this will result in a heterogeneous solution, where firms produce different quantities (note that they are still locally homogeneous, that is within the firm's own pool all the strings are identical).

== Design ==

After all agent'sagents have made a quantity production decision, the quantities are aggregated and plugged into a demand function to get a price. Each firm's profit is then calculated. Fitness values are then calculated as a function of profits. After the offspring pool is generated, hypothetical fitness values are calculated. These hypothetical values are based on some sort of estimation of the price level, often just by taking the previous price level.

The genetic algorithm generally consists of a population of n agents with m strings. These strings are often initially randomly generated but are then updated every g periods. Each string is assigned a fitness value through a defined method which is used as a measure of performance. The strings are updated through a series of operators. The basic genetic algorithm generally consists of three unique operators: the reproduction operator, which attempts to imitate successful agents and the two experimentation operators, crossover and mutation, which are implemented to bring diversity into the system. The augmented genetic algorithm includes an election operator, which adds a selection criteria.

===See Reproduction =also==

*{{slink|List of genetic algorithm applications #Finance and Economics}}

The first operator, reproduction, works by attempting to imitate. In general, it selects another agent to observe its fitness value. If its fitness value is greater than its own, then it elects to adopt the other agent's string. Otherwise, it preserves it own. These strings are then placed into an offspring pool to undergo the mutation operators, crossover and mutation. Most functions are [[stochastic]] and designed so that a small proportion of less fit solutions are selected. This helps keep the diversity of the population large, preventing premature convergence on poor solutions. Popular and well-studied selection methods include [[fitness proportionate selection|roulette wheel selection]] and [[tournament selection]].

=== Crossover ===

{{main|crossover (genetic algorithm)}}

=== Mutation ===

{{main|mutation (genetic algorithm)}}

=== Election ===

These processes ultimately result in the offspring pool of strings that is different from the initial parent pool. The election operator then works by comparing the fitness of the parent strings to the potential fitness of the offspring pool. If the offspring string has a higher fitness value, it will replace the parent string in the population. Otherwise, the parent string will stay. Generally the average fitness will have increased by this procedure for the population, since only the best strings are selected.

== Genetic Algorithm in the Cobweb Model ==

The cobweb model is a simple supply and demand model for a good over t periods. Firms (agents) make a production quantity decision in a given period, however their output is not produced until the following period. Thus, the firms are going to have to use some sort of method to forecast what the future price will be. The GA is used as a sort of learning behaviour for the firms. Initially their quantity production decisions are random, however each period they learn a little more. The result is the agents converge within the area of the [[rational expectations]] equilibrium (RATEX) for the stable and unstable case. If the election operator is used, the GA converges exactly to the RATEX equilibrium.

There are two type of learning methods these agents can be deployed with: social learning and individual learning. In social learning, each firm is endowed with a single string (which is used as its quantity production decision). It then compares this string against other firm's strings. In the individual learning case, agents are endowed with a pool strings. These strings are then compared against other strings within the agent's population pool. This can be thought of as mutual competing ideas within a firm whereas in the social case, it can be thought of as firm's learning from more successful firms. Note that in the social case and in the individual learning case with identical cost functions, that this is a homogeneous solution, that is all agent's production decisions are identical. However, if the cost functions are not identical, this will result in a heterogeneous solution, where firms produce different quantities (note that they are still locally homogeneous, that is within the firm's own pool all the strings are identical).

After all agent's have made a quantity production decision, the quantities are aggregated and plugged into a demand function to get a price. Each firm's profit is then calculated. Fitness values are then calculated as a function of profits. After the offspring pool is generated, hypothetical fitness values are calculated. These hypothetical values are based on some sort of estimation of the price level, often just by taking the previous price level.

== See Also ==

*[[Genetic Algorithm]]

*[[cobweb model]]

== References ==

* J H Miller, 'A Genetic Model of Adaptive Economic Behavior', University of Michigan working paper, 1986.

* J Arifovic, 'Genetic Algorithm Learning and the Cobweb Model ', Journal of Economic Dynamics and Control, vol. 18, Issue 1, (January 1994), 3-28.

* J Arifovic, 'Learning by Genetic Algorithm in Economic Environments', PhD Thesis, University of Chicago, 1991.

* J Arifovic, 'Genetic Algorithm Learning and the Cobweb Model ', Journal of Economic Dynamics and Control, vol. 18, Issue 1, (January 1994), 3-–28.

* R Hoffmann, 'The independent localisations of interaction and learning in the repeated prisoner's dilemma', Theory and Decision, vol. 47, p. 57–72, 1999.

* R Hoffmann, 'The ecology of cooperation', Theory and Decision, vol. 50, Issue 2. p. 101–118, 2001.

== External Links links==

* [httphttps://www.sfu.ca/crabe/ Centre for Adaptive Behaviour in Economics]

* [httphttps://wwwwww2.econ.iastate.edu/tesfatsi/getalife.htm Agent-Based Computational Economics and Artificial Life: A Brief Intro]

[[Category:EconometricsComputational economics]]

[[Category:Genetic algorithms|Production economics]]

[[Category:ArtificialGenetic intelligencealgorithms]]

[[Category:IntelligenceOptimization algorithms and methods]]

[[Category:Optimization algorithms]]